# superpos - 1 On the Application of Superposition to...

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1 On the Application of Superposition to Dependent Sources in Circuit Analysis W. Marshall Leach, Jr. c circlecopyrt Copyright 1994-2009. All rights reserved. Abstract —Many introductory circuits texts state or imply that superposition of dependent sources cannot be used in linear circuit analysis. Although the use of superposition of only independent sources leads to the correct solution, it does not make use of the full power of superposition. The use of superposition of dependent sources often leads to a simpler solution than other techniques of circuit analysis. A formal proof is presented that superposition of dependent sources is valid provided the controlling variable is not set to zero when the source is deactivated. Several examples are given which illustrate the technique. Index Terms — Circuit analysis, superposition, dependent sources, controlled sources I. P REFACE When he was a sophomore in college, the author was re- quired to take two semesters of circuit theory. The text was a reproduction of a set of typewritten notes written by Ronald E. Scott which were published later that year as a hard bound text [18]. The chapter that covered superposition had a num- ber of problems where the student was instructed to write by inspection the solution for a voltage or a current by using only superposition, Ohm’s law, voltage division, and current divi- sion. The author found these problems to be fascinating and he spent hours mastering them. In describing the principle of superposition, Scott only had independent sources in his circuits. However, the author found that he could also solve circuits containing controlled sources using superposition. Later, after becoming a teacher, he was challenged by students when he used these techniques in teach- ing electronics courses. The students said that they had been taught that superposition with controlled sources was not al- lowed. The students were easily satisfied when they were shown that a node voltage analysis yields the same solution. After encountering so many challenges by students, the au- thor researched circuits books in the library at his school and at a store of a large bookstore chain. None of the books said that superposition can be used with controlled sources. Indeed, the majority stated clearly that it could not. Thinking that other educators might find the topic to be inter- esting and useful, the author submitted a paper on the topic to the IEEE Trans. on Education in early 1994. It was rejected af- ter the reviewer conceived a circuit that it could not be applied to. The reviewer’s circuit contained a fl oating node at which The author is with the School of Electrical and Computer Engineering at the Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. Email: [email protected]

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